Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras

We propose factorized difference operators L(u) associated with the twisted quantum affine algebras U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}), U_{q}(D^{(2)}_{n+1}),U_{q}(D^{(3)}_{4}). These operators are shown to be annihilated by a screening operator. Based on a basis of the solutions of the difference equation L(u)w(u)=0, we also construct a Casorati determinant solution to the T-system for U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}).Comment: 15 page

Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model

We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer matrix. These TBA equations are identical to the ones from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIE). In particular, a subset of these NLIE forms a system of NLIE which contains only a finite number of unknown functions. For r=1, this subset of NLIE reduces to Takahashi's NLIE for the XXX spin chain. A relation between the traditional TBA equations and our new NLIE is clarified. Based on our new NLIE, we also calculate the high temperature expansion of the free energy.Comment: 24 pages, 4 figures, to appear in J. Phys. A: Math. Ge

Baxter's Q-operators and operatorial Backlund flow for quantum (super)-spin chains

We propose the operatorial form of Baxter's TQ-relations in a general form of the operatorial B\"acklund flow describing the nesting process for the inhomogeneous rational gl(K|M) quantum (super)spin chains with twisted periodic boundary conditions. The full set of Q-operators and T-operators on all levels of nesting is explicitly defined. The results are based on a generalization of the identities among the group characters and their group co-derivatives with respect to the twist matrix, found by one of the authors and P.Vieira [V.Kazakov and P.Vieira, JHEP 0810 (2008) 050 [arXiv:0711.2470]]. Our formalism allows a systematic and rather straightforward derivation of the whole set of nested Bethe ansatz equations for the spectrum of quantum integrable spin chains, starting from the R-matrix

Exact results for the thermal and magnetic properties of strong coupling ladder compounds

We investigate the thermal and magnetic properties of the integrable su(4) ladder model by means of the quantum transfer matrix method. The magnetic susceptibility, specific heat, magnetic entropy and high field magnetization are evaluated from the free energy derived via the recently proposed method of high temperature expansion for exactly solved models. We show that the integrable model can be used to describe the physics of the strong coupling ladder compounds. Excellent agreement is seen between the theoretical results and the experimental data for the known ladder compounds (5IAP)$_2$CuBr$_4$$\cdot$2H$_2$O, Cu$_{2}$(C$_5$H$_{12}$N$_2$)$_2$Cl$_4$ etc.Comment: 10 pages, 5 figure

Nonlinear integral equations for the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model

We derive a finite set of nonlinear integral equations (NLIE) for the thermodynamics of the one-dimensional sl(4)-symmetric Uimin-Sutherland model. Our NLIE can be evaluated numerically for arbitrary finite temperature and chemical potentials. We recover the NLIE for sl(3) as a limiting case. In comparison to other recently derived NLIE, the evaluation at low temperature poses no problem in our formulation. The model shows a rich ground-state phase diagram. We obtain the critical fields from the T to zero limit of our NLIE. As an example for the application of the NLIE, we give numerical results for the SU(4) spin-orbital model. The magnetic susceptibility shows divergences at critical fields in the low-temperature limit and logarithmic singularities for zero magnetic field.Comment: 32 pages, 7 figures; references added, minor corrections, final versio

Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds

(abbreviated) This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of real compounds. The ground state properties of the integrable two-leg spin-1/2 and the mixed spin-(1/2,1) ladder models at zero temperature are analyzed by means of the Thermodynamic Bethe Ansatz. Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are investigated in terms of the recently introduced High Temperature Expansion method, which is discussed in detail. It is shown that in the strong coupling limit the integrable spin-1/2 ladder model exhibits three quantum phases: (i) a gapped phase in the regime $H<H_{c1}$, (ii) a fully polarised phase for $H>H_{c2}$, and (iii) a Luttinger liquid magnetic phase in the regime $H_{c1}<H<H_{c2}$. The critical behaviour in the vicinity of the critical points is of the Pokrovsky-Talapov type. The temperature-dependent thermal and magnetic properties are directly evaluated from the exact free energy expression and compared to known experimental results for a range of strong coupling ladder compounds. Similar analysis of the mixed spin-(1/2,1) ladder model reveals a rich phase diagram, with a 1/3 and a full saturation magnetisation plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetisation plateau is diminished and a new quantum phase transition occurs. The phase diagram can be directly deduced from the magnetisation curve obtained from the exact result derived from the HTE. The thermodynamics of the spin-orbital model with different single-ion anisotropies is also investigated.Comment: 90 pages, 33 figures, extensive revisio

From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model

We propose a nonlinear integral equation (NLIE) with only one unknown function, which gives the free energy of the integrable one dimensional Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum Jacobi-Trudi and Giambelli formula (Bazhanov-Reshetikhin formula), which gives the solution of the T-system, plays an important role. In addition, we also calculate the high temperature expansion of the specific heat and the magnetic susceptibility.Comment: 18 pages, LaTeX; some explanations, 2 figures, one reference added; typos corrected; to appear in J. Phys. A: Math. Ge

Condensation of 4-hydroxy-2-thiazolines with 1,2-phenylenediamine as a novel effective route to thiazolo[3,4-a]quinoxalines

Thiazolo[3,4-a]quinoxalin-4-ones were prepared in two steps starting from methyl phenylchloropyruvate using a new strategy for the construction of the ring system. A key step in this new method involves the reaction of 4-hydroxytetrahydrothiazoles with 1,2-phenylendiamines